Finite Group Databasebeta

← #21446740

Subgroups — #21446740

Order 7808.

324 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519775C211yesmaximal, characteristic
2C2×#14519706C211yesmaximal, characteristic
3C2×#14519702C211yesmaximal, characteristic
4C2×#14519701C211yesmaximal, characteristic
5C2×#14519700C211yesmaximal, characteristic
6C4⋊C4×Dic61C211yesmaximal, characteristic
7C2×#103×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519775—22no—
11#14519775C414yescomplemented
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196—21no—
14C2×#11758196—21no—
15C2×C4×Dic61—21no—
16C2×C4×Dic61C2211yescharacteristic
17#14519706—22no—
18#14519702—22no—
19#14519701—22no—
20#14519700—22no—
21#14519684—21no—
22C22×Q8×C61C2211yescharacteristic
23C22×C8×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25#103×C61—22no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61C2×C412yes—
32C22×C4×C61—21no—
33C22×C4×C61—21no—
34C22×C4×C61C2311yescharacteristic
35C22×Dic61—21no—
36C22×Dic61—21no—
37C22×Dic61D411yescharacteristic
38C22×Dic61D411yescharacteristic
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122—21no—
42C2×Dic122—21no—
43C2×Dic122—21no—
44C2×Dic122C2×C412yes—
45C2×C8×C61—21no—
46C2×C8×C61—21no—
47C2×C8×C61—21no—
48C4⋊C4×C61—21no—
49C4⋊C4×C61D412yes—
50C4⋊Dic61—21no—
51C4⋊Dic61D412yes—
52#11758196—24no—
53#11758196—24no—
54C4×Dic61—42no—
55C4×Dic61C2×C412yes—
56C4×Dic61D412yes—
57C2×#92418—21no—
58C2×#92418—21no—
59C2×#92418—21no—
60C23×C61C2×D411yescharacteristic
61Q8×C61—22no—
62Q8×C61—22no—
63Q8×C61—41no—
64Q8×C61—41no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61C22×C411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C2×C4×C61#4111yescharacteristic
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61—41no—
85C2×Dic61C22⋊C412yes—
86C2×Dic61C22⋊C412yes—
87C2×Dic61SD1612yes—
88C2×Dic61Q1612yes—
89Dic122—22no—
90Dic122—22no—
91Dic122—41no—
92Dic122—41no—
93C8×C61—41no—
94#92418—41no—
95C22×C61C2×C22⋊C411yescharacteristic
96C22×C61#12111yescharacteristic
97C22×C61#12111yescharacteristic
98C22×C61C2×SD1611yescharacteristic
99C22×C61C2×Q1611yescharacteristic
100C22×C61#13711yescharacteristic
101C22×C61#13711yescharacteristic
102C4×C61—42no—
103C4×C61—42no—
104C4×C61C4×D411yescharacteristic
105C4×C61C4×D411yescharacteristic
106C4×C61#12411yescharacteristic
107C4×C61#12711yescharacteristic
108Dic61—22no—
109Dic61—42no—
110Dic61—42no—
111Dic61#10314yescomplemented
112#1981—611nomaximal, Sylow
113C2×C61#39011yescharacteristic
114C2×C61C2×#10311yescharacteristic
115C2×C61#41911yescharacteristic
116C2×C61#46111yescharacteristic
117C2×C61#46111yescharacteristic
118C2×C61#46211yescharacteristic
119C2×C61#46211yescharacteristic
120C2×C4⋊Q8—611no—
121C2×C4⋊C8—611no—
122C2×#103—611no—
123C2×#103—611no—
124C2×#103—611no—
125C2×#103D6111yescharacteristic
126C4×C4⋊C4—611no—
127C61#198111yescharacteristic, complemented, Sylow
128C22×Q8—611no—
129C22×Q8C2×D6111yescharacteristic
130C22×C8—611no—
131C22×C8C2×D6111yescharacteristic
132C4⋊Q8—614no—
133C4⋊Q8—1222no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—1221no—
136C2×C4⋊C4—1221no—
137C2×C4⋊C4C2×D6111yescharacteristic
138C2×C42—611no—
139C2×C42—1221no—
140C4⋊C8—1222no—
141#103—22no—
142#103—1222no—
143#103—1222no—
144#103—1222no—
145#95—1221no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—612no—
152C2×Q8—1221no—
153C2×Q8—1221no—
154C2×Q8—1221no—
155C2×Q8—1221no—
156C2×Q8—1221no—
157C2×Q8C4×D6112yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—1221no—
163C22×C4—1221no—
164C22×C4C22×D6111yescharacteristic
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—1221no—
169C2×C8—1221no—
170C2×C8—1221no—
171C4⋊C4—21no—
172C4⋊C4—612no—
173C4⋊C4—1224no—
174C4⋊C4—1224no—
175C4⋊C4—1221no—
176C4⋊C4C22⋊D6112yes—
177C42—612no—
178C42—612no—
179C42—2442no—
180C23D4×D6111yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—41no—
184Q8—41no—
185Q8—1222no—
186Q8—1222no—
187Q8—2441no—
188Q8—2441no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—612no—
196C2×C4—612no—
197C2×C4—612no—
198C2×C4—612no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4—2441no—
207C2×C4C2×C4×D6111yescharacteristic
208C2×C4#1175822211yescharacteristic
209C2×C4D4×D6111yescharacteristic
210C2×C4D4×D6111yescharacteristic
211C2×C4#1175822411yescharacteristic
212C2×C4C2×C22⋊D6111yescharacteristic
213C8—41no—
214C8—2441no—
215C22C22⋊C4×D6111yescharacteristic
216C22#1451974911yescharacteristic
217C22#1451975011yescharacteristic
218C22SD16×D6111yescharacteristic
219C22Q16×D6111yescharacteristic
220C22#1451980611yescharacteristic
221C22#1451980911yescharacteristic
222C4—42no—
223C4—42no—
224C4—614no—
225C4—1222no—
226C4—2442no—
227C4—2442no—
228C4#1451973711yescharacteristic
229C4C4×C22⋊D6111yescharacteristic
230C4#1451976311yescharacteristic
231C4#1451977311yescharacteristic
232C2#1683966211yescharacteristic
233C2#103×D6111yescharacteristic
234C2#1683976911yescharacteristic
235C2#1683996511yescharacteristic
236C2#1683996611yescharacteristic
237C2#1683997011yescharacteristic
238C2#1683997111yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61#1981
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
11. #14519775C4semidirect
111. Dic61#103semidirect
127. C61#1981semidirect